Benhassine, Abderrazek2021-12-172021-12-172018-01-04Benhassine, A. (2018). Fractional Schrödinger equations with new conditions. <i>Electronic Journal of Differential Equations, 2018</i>(05), pp. 1-12.1072-6691https://hdl.handle.net/10877/15060In this article, we study the nonlinear fractional Schrödinger equation (-∆)αu + V(x)u = ƒ(x, u) u ∈ Hα (ℝn, ℝ), where (-∆)α(α ∈ (0, 1)) stands for the fractional Laplacian of order α, x ∈ ℝn, V ∈ C(ℝn, ℝ) may change sign and ƒ is only locally defined near the origin with respect to u. Under some new assumptions on V and ƒ, we show that the above system has infinitely many solutions near the origin. Some examples are also given to illustrate our main theoretical result.Text12 pages1 file (.pdf)enAttribution 4.0 InternationalFractional Schrödinger equationsCritical point theorySymmetric mountain pass theoremArticle